manylinux_2_34 is built on AlmaLinux 9. Alma Linux is built for the x86-64-v2 sub-architecture, which assumes that a particular set of x86-64 CPU extensions. (See https://developers.redhat.com/blog/2021/01/05/building-red-hat-enterprise-linux-9-for-the-x86-64-v2-microarchitecture-level#recommendations_for_rhel_9)

As a result, wheels built in manylinux_2_34 by the system compiler will use these CPU extensions, making the wheels not compatible with all x86-64 CPUs, which of course results will result in SIGILL at runtime.

Because wheel tags have no awareness of x86-64-v2, this effectively makes binaries built with manylinux_2_34 unusable.

See pyca/cryptography#12069 for an example of the impact of this.